What is wrong with mesh PCA in coordinate direction normalization
Introduction
Recently, there has been a constant increasing interest on surface registration for 3D pattern analysis. As in surface registration the same 3D model will have different representation if using different coordinate frames, coordinate frame normalization needs to be accomplished at first. Among all coordinate frame normalization processing, coordinate direction normalization is the most important process. For this task, mesh PCA is widely used in determining the direction transformation matrix in coordinate frame direction normalization (see Refs. [1], [2] to cite a few).
However, although mesh PCA method can always produce three principal axes for direction normalization, the results of coordinate transformation are uncertainty. Although work in [3] gives a simple discuss on the property, it is far from adequate explanation. In our work we analyze such reasons exhaustively by discrete signal statistical view [4]. We present an improved mesh PCA method inspired by the fact that the principal axes directions of 3D surface should be those in which the vertex distances are the longest among all 3D vertex distances. Six coordinate transformation matrixes are used, respectively, in different cases for coordinate axes adjusting. Thus, mesh PCA uncertainty will be alleviated well.
Section snippets
Uncertainty of mesh PCA
In this section, we first make a detailed analysis on mesh PCA uncertainty in the view of statistical signal analysis. And we conclude that three dominant factors affect the mesh PCA uncertainty. Then we present our method to improve mesh PCA results in 3D surface registration.
Experimental results
We first use synthetic 3D models, coming from multi-view image reconstruction (vertice numbers are about 100–300, mesh numbers are about 200–500), to show uncertainty of mesh PCA. Meshes will be subdivided or simplified in different sizes when needed. Fig. 1 shows such model direction normalization results. Experimental results on range data (vertice numbers are about 5000–8000, mesh numbers are about 10 000–20 000) are also proved in Fig. 2. Every model mesh PCA uncertainty guideline is
Conclusion
We have made a detailed analysis on mesh PCA uncertainty in coordinate direction normalization for 3D surface registration. We present a fast method to improve mesh PCA result based on the vertex distance longest selection principles. By six rotation transformation, our method partially overcomes the problem on mesh PCA uncertainty.
In fact, as PCA is a lineal technology essentially, mesh PCA method will face more challenging problems on coordinate direction normalization procedure. Thus we will
Acknowledgments
This work is supported by National Natural Science Foundation of China (No. 60402020). In addition, we would like to thank for all those people who have contributed to this work by providing their data and comments.
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